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A097727
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Pell equation solutions (5*b(n))^2 - 26*a(n)^2 = -1 with b(n):=A097726(n), n>=0.
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7
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1, 101, 10301, 1050601, 107151001, 10928351501, 1114584702101, 113676711262801, 11593909964103601, 1182465139627304501, 120599850332020955501, 12300002268726510156601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hypotenuses of primitive Pythagorean triples in A195622 and A195623. - Clark Kimberling, Sep 22 2011
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= S(n, 2*51) - S(n-1, 2*51) = T(2*n+1, sqrt(26))/sqrt(26), with Chebyshev polynomials of the 2nd and first kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle.
a(n)= ((-1)^n)*S(2*n, 10*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-102*x+x^2).
a(n)=102*a(n-1)-a(n-2) for n>1 ; a(0)=1, a(1)=101 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| (x,y) = (5,1), (515,101), (52525,10301), ... give the positive integer solutions to x^2 - 26*y^2 =-1.
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CROSSREFS
| Cf. A097725 for S(n, 102).
Row 5 of array A188647.
Sequence in context: A071783 A082808 A100027 * A083981 A138148 A138831
Adjacent sequences: A097724 A097725 A097726 * A097728 A097729 A097730
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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